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# What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?

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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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23 Jun 2016, 11:21
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What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)
[Reveal] Spoiler: OA

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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23 Jun 2016, 11:28
B. 12

(x-12) (x+8) so solutions are 12, -8

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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23 Jun 2016, 11:30
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2$$ − $$4x$$ = $$96$$

Or, $$x^2$$ − $$4x$$ − $$96$$ = 0

Or, $$x^2$$ $$−12x$$ + $$8x$$ − $$96$$ = 0

Or, x ( x - 12 ) + 8 ( x - 12 ) = 0

Or x = 12 , -8

So , The larger of the 2 solutions must be (B) 12

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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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24 Jun 2016, 03:00
Solving Quadratic equation $$x^2 − 4x = 96$$

$$x^2 - 4x - 96 = 0$$

$$x^2 - 12x - 8x - 96 = 0$$

x (x - 12) + 8 (x - 12) = 0

(x + 8) (x - 12)

x = 12, -8

x=12 is larger value

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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14 Apr 2017, 07:19
Simply set the quadratic equation to zero and factor the roots out.

$${ x }^{ 2 }-4x=96\\ { x }^{ 2 }-4x-96=0\\ \left( x+8 \right) \left( x-12 \right) =0\\ x=-8,\quad x=12$$

For those people, like me, who struggle to find the roots, I suggest using one approach I took from pacifist85.

Prime factorize the constant and see which number combinations that sum to 4 and multiply to 96.

$$96={ 2 }^{ 5 }\ast { 3 }^{ 1 }$$

You will eventually find the 8 and 12 roots.
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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14 Apr 2017, 07:30
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2 − 4x = 96$$

Or, $$x^2 − 4x − 96 = 0$$

Or, $$x^2 − x ( 12 − 8 ) − 96 = 0$$

Or, $$x^2 − 12x + 8x − 96 = 0$$

Or, $$x ( x − 12 ) + 8( x − 12 ) = 0$$

So, $$x = 12$$ , $$− 8$$

Thus, larger of the 2 numbers is 12 , answer must be (B) 12
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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09 Jun 2017, 14:12
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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

$$x^2 - 4x - 96 = 0$$
$$x^2 - 4x + 4 - 100 = 0$$
$$(x-2)^2 = 100$$
$$x-2 = 10$$ or $$x-2 = -10$$
roots are 12 and -8, with 12 being the larger. => Answer B

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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12 Jun 2017, 18:59
The solution should be one of the roots of x^2−4x−96=0

Working from the answer choices, we can work backwards to see if we get an integer quotient by dividing 96 by the answer choice and then checking if we can get a -4 as the difference between the quotient and the answer choice.

Only B fits the scenarios as 96/12 = 8 and 12-8 is 4.

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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31 Oct 2017, 23:50
I have a question here. So in the equation given : x^2 - 4x =96 then x(x-4)=96 therefore x=96 or x-4=96 x=100
I know for the fact that this method is incorrect. But am not understanding why is it incorrect. can someone please help me

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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01 Nov 2017, 01:23
x^2−4x=96 => (x-12)*(x+8) = 0. > x = 12 or x = -8 => answer B

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]

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02 Nov 2017, 15:58
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

x^2 - 4x - 96 = 0

(x + 8)(x - 12) = 0

x = -8 or x = 12

The larger of the two solutions is 12.

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?   [#permalink] 02 Nov 2017, 15:58
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